Round-off error

In mathematics, a round-off error, also called rounding error, is the difference between the calculated approximation of a number and its exact mathematical value due to rounding.

Description

Round-off error is a form of quantization error.

One of the goals of numerical analysis is to estimate errors in calculations, including round-off error, when using approximation equations and/or algorithms, especially when using finitely many digits to represent real numbers (which in theory have infinitely many digits).

When a sequence of calculations subject to rounding error is made, errors may accumulate, sometimes dominating the calculation. In ill-conditioned problems, significant error may accumulate.

Representation error

The error introduced by attempting to represent a number using a finite string of digits is a form of round-off error called representation error.

See also

• Algorithm
• Approximation
• Computer science
• Error analysis (mathematics)
• Mathematics
• Numerical analysis
• Numerical stability
• Rounding

External links

• Round-off error @ Wikipedia